Four Ships
12 Sep 2008
Puzzle

Four ships are sailing on a 2D planet. Each ships traverses a straight line at constant speed. No two ships are traveling parallel to each other. Their journeys started at some time in the distant past. Sometimes, a pair of ships collides. A ship continues its journey even after a collision. However, it is strong enough only to survive two collisions; it dies when it collides a third time. The situation is grim. Five of six possible collisions have already taken place (no collision involved more than 2 ships) and two ships are out of commission. What fate awaits the remaining two?

Source

I first heard this puzzle from Sanjeeb Dash in 1994 when we were together at IIT Delhi. Sanjeeb is presently at IBM Research.

Solution

Let z-axis denote time. Let x- and y- axes denote the 2D planet. Then the four trajectories are straight lines. Since no collision involved more than two ships, these four lines must all lie in a plane. So the sixth collision is certain.

© Copyright 2008—2018, Gurmeet Manku.